In the old days, those would have been mounted police. People get out of the way of horses. They do not get out of the way of bicycles. In fact, everyone I know giggles when they see a cop with a bike.
Horses do work better though. They are still widely used in NOLA. Even the drunks get out of the way.
The NOLA PD still uses mounted police and I’d bet serious money a big reason is crowd control in the Quarter.
Sometimes they have no choice. I was just a teen in 1948 when I saw the NYC police breakup a May Day melee. The mounted cops came in parallel to the mob and then had the horse use his rear end to shove the people aside.
I saw foot police club a couple of women who were wearing big floppy hat and asked my dad why they did that. He said the women had big pins to hold their hats on and used them to stick the horses. (They were Communists.)